A coupling apparatus presses conical members having curved surfaces in a direction perpendicular to reinforcing bars by using hydraulic pressure, thereby considerably reducing working time for coupling reinforcing bars, completely securing the reinforcing bars and increasing compressive and bending strength. It is possible to stably carry force from the conical members through external force dispersion medium members to reinforcing bar securing members. Accordingly, there is a structural advantage of effectively preventing the displacement and the loosening of the coupled reinforcing bars.